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<h1 class="mume-header" id="%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%85%B3%E8%81%94%E5%88%86%E6%9E%90indexhtml"><a href="./index.html">&#x673A;&#x5668;&#x5B66;&#x4E60;&#xFF1A;&#x5173;&#x8054;&#x5206;&#x6790;</a></h1>

<ul>
<li><a href="#%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%85%B3%E8%81%94%E5%88%86%E6%9E%90indexhtml">&#x673A;&#x5668;&#x5B66;&#x4E60;&#xFF1A;&#x5173;&#x8054;&#x5206;&#x6790;</a>
<ul>
<li><a href="#apriori">Apriori</a>
<ul>
<li><a href="#%E9%A2%91%E7%B9%81%E9%A1%B9%E9%9B%86">&#x9891;&#x7E41;&#x9879;&#x96C6;</a>
<ul>
<li><a href="#%E6%94%AF%E6%8C%81%E5%BA%A6">&#x652F;&#x6301;&#x5EA6;</a></li>
<li><a href="#%E7%BD%AE%E4%BF%A1%E5%BA%A6">&#x7F6E;&#x4FE1;&#x5EA6;</a></li>
<li><a href="#%E6%8F%90%E5%8D%87%E5%BA%A6">&#x63D0;&#x5347;&#x5EA6;</a></li>
</ul>
</li>
<li><a href="#apriori%E7%AE%97%E6%B3%95">Apriori&#x7B97;&#x6CD5;</a>
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<li><a href="#example">Example</a></li>
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<li><a href="#fp-tree">FP-tree</a>
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<li><a href="#fp-tree%E7%AE%97%E6%B3%95">FP-tree&#x7B97;&#x6CD5;</a>
<ul>
<li><a href="#example-1">Example</a></li>
</ul>
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<h2 class="mume-header" id="apriori">Apriori</h2>

<h3 class="mume-header" id="%E9%A2%91%E7%B9%81%E9%A1%B9%E9%9B%86">&#x9891;&#x7E41;&#x9879;&#x96C6;</h3>

<p>&#x9891;&#x7E41;&#x9879;&#x96C6;&#x7684;&#x8BC4;&#x4F30;&#x6807;&#x51C6;&#x6709;</p>
<h4 class="mume-header" id="%E6%94%AF%E6%8C%81%E5%BA%A6">&#x652F;&#x6301;&#x5EA6;</h4>

<p>&#x5173;&#x8054;&#x7684;&#x6570;&#x636E;&#x5728;&#x6570;&#x636E;&#x96C6;&#x4E2D;&#x51FA;&#x73B0;&#x7684;&#x6B21;&#x6570;&#x5360;&#x603B;&#x6570;&#x636E;&#x96C6;&#x7684;&#x6BD4;&#x91CD;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo></mrow><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>S</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\mathrm{Support}(X) = P(X) 
        = \frac{
            \mathrm{Count}(X)
        }{
            \mathrm{Count}(Samples)
        }</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">S</span><span class="mord mathrm">u</span><span class="mord mathrm">p</span><span class="mord mathrm">p</span><span class="mord mathrm">o</span><span class="mord mathrm">r</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">o</span><span class="mord mathrm">u</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault">a</span><span class="mord mathdefault">m</span><span class="mord mathdefault">p</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">e</span><span class="mord mathdefault">s</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">o</span><span class="mord mathrm">u</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo separator="true">,</mo><mi>Y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mi>Y</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>S</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi><mi>s</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\mathrm{Support}(X,Y) = P(XY) 
        = \frac{
            \mathrm{Count}(XY)
        }{
            \mathrm{Count}(Samples)
        }</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">S</span><span class="mord mathrm">u</span><span class="mord mathrm">p</span><span class="mord mathrm">p</span><span class="mord mathrm">o</span><span class="mord mathrm">r</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">o</span><span class="mord mathrm">u</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault">a</span><span class="mord mathdefault">m</span><span class="mord mathdefault">p</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">e</span><span class="mord mathdefault">s</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">o</span><span class="mord mathrm">u</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{Count}(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">o</span><span class="mord mathrm">u</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span>&#xFF1A;&#x8868;&#x793A;&#x7EDF;&#x8BA1;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">x</span></span></span></span>&#x7684;&#x6570;&#x91CF;</li>
</ul>
<h4 class="mume-header" id="%E7%BD%AE%E4%BF%A1%E5%BA%A6">&#x7F6E;&#x4FE1;&#x5EA6;</h4>

<p>&#x4E00;&#x4E2A;&#x6570;&#x636E;&#x51FA;&#x73B0;&#x540E;&#xFF0C;&#x53E6;&#x4E00;&#x4E2A;&#x6570;&#x636E;&#x51FA;&#x73B0;&#x7684;&#x6982;&#x7387;&#xFF0C;&#x5373;&#x6570;&#x636E;&#x7684;&#x6761;&#x4EF6;&#x6982;&#x7387;&#xFF08;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span></span></span></span>&#x5728;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span></span></span></span>&#x53D1;&#x751F;&#x7684;&#x6761;&#x4EF6;&#x4E0B;&#x53D1;&#x751F;&#x7684;&#x6982;&#x7387;&#xFF09;&#x3002;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo>&#x21D0;</mo><mi>Y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>Y</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo separator="true">,</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\mathrm{Confidence}(X &#x21D0; Y)
        = P(X {\ \bold|\ } Y)
        = \dfrac{
            \mathrm{Support}(X, Y)
        }{
            \mathrm{Support}(Y)
        }
        = \dfrac{
            P(XY)
        }{
            P(Y)
        }</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">o</span><span class="mord mathrm">n</span><span class="mord mathrm" style="margin-right:0.07778em;">f</span><span class="mord mathrm">i</span><span class="mord mathrm">d</span><span class="mord mathrm">e</span><span class="mord mathrm">n</span><span class="mord mathrm">c</span><span class="mord mathrm">e</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">S</span><span class="mord mathrm">u</span><span class="mord mathrm">p</span><span class="mord mathrm">p</span><span class="mord mathrm">o</span><span class="mord mathrm">r</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">S</span><span class="mord mathrm">u</span><span class="mord mathrm">p</span><span class="mord mathrm">p</span><span class="mord mathrm">o</span><span class="mord mathrm">r</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h4 class="mume-header" id="%E6%8F%90%E5%8D%87%E5%BA%A6">&#x63D0;&#x5347;&#x5EA6;</h4>

<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span></span></span></span>&#x5728;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span></span></span></span>&#x53D1;&#x751F;&#x7684;&#x6761;&#x4EF6;&#x4E0B;&#x53D1;&#x751F;&#x7684;&#x6982;&#x7387;&#xFF0C;&#x4E0E;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span></span></span></span>&#x603B;&#x4F53;&#x53D1;&#x751F;&#x7684;&#x6982;&#x7387;&#x4E4B;&#x6BD4;</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo>&#x21D0;</mo><mi>Y</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi>C</mi><mi>o</mi><mi>n</mi><mi>f</mi><mi>i</mi><mi>d</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mo stretchy="false">(</mo><mi>X</mi><mo>&#x21D0;</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mi>Y</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>Y</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\mathrm{Lift}(X &#x21D0; Y)
        = \dfrac{
            Confidence(X &#x21D0; Y)
        }{
            P(X)
        }
        = \dfrac{ 
            P(X {\ \bold|\ } Y)
        }{ 
            P(X)
        }
        = \dfrac{
            P(XY)
        }{
            P(X)P(Y)
        }</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">L</span><span class="mord mathrm">i</span><span class="mord mathrm" style="margin-right:0.07778em;">f</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord mathdefault">o</span><span class="mord mathdefault">n</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mord mathdefault">i</span><span class="mord mathdefault">d</span><span class="mord mathdefault">e</span><span class="mord mathdefault">n</span><span class="mord mathdefault">c</span><span class="mord mathdefault">e</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<table>
<thead>
<tr>
<th>&#x63D0;&#x5347;&#x5EA6;</th>
<th>&#x5173;&#x8054;&#x5F3A;&#x5F31;</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo>&#x21D0;</mo><mi>Y</mi><mo stretchy="false">)</mo><mo>&gt;</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathrm{Lift}(X &#x21D0; Y) &gt; 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">L</span><span class="mord mathrm">i</span><span class="mord mathrm" style="margin-right:0.07778em;">f</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mo>&#x21D0;</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">X &#x21D0; Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span></span></span></span>&#x4E3A;&#x6709;&#x6548;&#x7684;&#x5F3A;&#x5173;&#x8054;</td>
</tr>
<tr>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">t</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo>&#x21D0;</mo><mi>Y</mi><mo stretchy="false">)</mo><mo>&lt;</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathrm{Lift}(X &#x21D0; Y) &lt; 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">L</span><span class="mord mathrm">i</span><span class="mord mathrm" style="margin-right:0.07778em;">f</span><span class="mord mathrm">t</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span></td>
<td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mo>&#x21D0;</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">X &#x21D0; Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span></span></span></span>&#x4E3A;&#x65E0;&#x6548;&#x7684;&#x5F3A;&#x5173;&#x8054;</td>
</tr>
</tbody>
</table>
<p><span class="highlight">&#x8981;&#x9009;&#x62E9;&#x4E00;&#x4E2A;&#x6570;&#x636E;&#x96C6;&#x5408;&#x4E2D;&#x7684;&#x9891;&#x7E41;&#x6570;&#x636E;&#x96C6;&#xFF0C;&#x5219;&#x9700;&#x8981;&#x81EA;&#x5B9A;&#x4E49;&#x8BC4;&#x4F30;&#x6807;&#x51C6;&#x3002;&#x6700;&#x5E38;&#x7528;&#x7684;&#x8BC4;&#x4F30;&#x6807;&#x51C6;&#x662F;&#x7528;&#x81EA;&#x5B9A;&#x4E49;&#x7684;<strong>&#x652F;&#x6301;&#x5EA6;</strong>&#xFF0C;&#x6216;&#x8005;&#x662F;&#x81EA;&#x5B9A;&#x4E49;<strong>&#x652F;&#x6301;&#x5EA6;</strong>&#x548C;<strong>&#x7F6E;&#x4FE1;&#x5EA6;</strong>&#x7684;&#x4E00;&#x4E2A;&#x7EC4;&#x5408;&#x3002;</span></p>
<h3 class="mume-header" id="apriori%E7%AE%97%E6%B3%95">Apriori&#x7B97;&#x6CD5;</h3>

<p>Apriori&#x7B97;&#x6CD5;&#x662F;&#x5E38;&#x7528;&#x7684;&#x7528;&#x4E8E;&#x6316;&#x6398;&#x51FA;&#x6570;&#x636E;&#x5173;&#x8054;&#x89C4;&#x5219;&#x7684;&#x7B97;&#x6CD5;&#xFF0C;&#x5B83;&#x7528;&#x6765;&#x627E;&#x51FA;&#x6570;&#x636E;&#x503C;&#x4E2D;&#x9891;&#x7E41;&#x51FA;&#x73B0;&#x7684;&#x6570;&#x636E;&#x96C6;&#x5408;&#x3002;</p>
<p>Apriori&#x7B97;&#x6CD5;&#x7684;&#x76EE;&#x6807;&#x662F;&#x627E;&#x5230;&#x6700;&#x5927;&#x7684;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi></mrow><annotation encoding="application/x-tex">K</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">K</span></span></span></span>&#x9879;&#x9891;&#x7E41;&#x96C6;&#x3002;</p>
<blockquote>
<ul>
<li>&#x5982;&#x679C;&#x4E00;&#x4E2A;&#x96C6;&#x5408;&#x662F;&#x9891;&#x7E41;&#x9879;&#x96C6;&#xFF0C;&#x5219;&#x5B83;&#x7684;&#x6240;&#x6709;&#x975E;&#x7A7A;&#x5B50;&#x96C6;&#x90FD;&#x662F;&#x9891;&#x7E41;&#x9879;&#x96C6;&#x3002;</li>
<li>&#x5982;&#x679C;&#x4E00;&#x4E2A;&#x96C6;&#x5408;&#x4E0D;&#x662F;&#x9891;&#x7E41;&#x9879;&#x96C6;&#xFF0C;&#x5219;&#x5B83;&#x7684;&#x6240;&#x6709;&#x8D85;&#x96C6;&#x90FD;&#x4E0D;&#x662F;&#x9891;&#x7E41;&#x9879;&#x96C6;&#x3002;</li>
</ul>
</blockquote>
<ul>
<li><em><strong>Step1</strong></em>&#xFF1A;&#x627E;&#x5230;&#x7B26;&#x5408;&#x652F;&#x6301;&#x5EA6;&#x6807;&#x51C6;&#x7684;&#x9891;&#x7E41;&#x96C6;</li>
<li><em><strong>Step2</strong></em>&#xFF1A;&#x627E;&#x5230;&#x6700;&#x5927;&#x4E2A;&#x6570;&#x7684;&#x9891;&#x7E41;&#x96C6;</li>
</ul>
<h4 class="mume-header" id="example">Example</h4>

<p>&#x89C4;&#x5B9A;&#x6700;&#x5C0F;&#x652F;&#x6301;&#x8BA1;&#x6570;&#x4E3A;2</p>
<p><img src="images/relation_Apriori_eg1.png" alt></p>
<h2 class="mume-header" id="fp-tree">FP-tree</h2>

<p>&#x968F;&#x7740;&#x6570;&#x636E;&#x5E93;&#x5BB9;&#x91CF;&#x7684;&#x589E;&#x5927;&#xFF0C;<strong>Apriori&#x7B97;&#x6CD5;</strong>&#x91CD;&#x590D;&#x8BBF;&#x95EE;&#x6570;&#x636E;&#x5E93;&#xFF08;&#x5916;&#x5B58;&#xFF09;&#x5C06;&#x5BFC;&#x81F4;&#x6027;&#x80FD;&#x4F4E;&#x4E0B;&#x3002;<strong>FP-tree&#x7B97;&#x6CD5;</strong>&#x5BF9;&#x6B64;&#x8FDB;&#x884C;&#x4E86;&#x6539;&#x8FDB;&#xFF0C;&#x51CF;&#x5C11;&#x4E86;&#x6570;&#x636E;&#x5E93;&#x7684;&#x626B;&#x63CF;&#x6B21;&#x6570;&#x548C;&#x4FAF;&#x9009;&#x96C6;&#x7A7A;&#x95F4;&#x5360;&#x7528;&#x3002;</p>
<h3 class="mume-header" id="fp-tree%E7%AE%97%E6%B3%95">FP-tree&#x7B97;&#x6CD5;</h3>

<ul>
<li><em><strong>Step1</strong></em>&#xFF1A;&#x7B2C;&#x4E00;&#x6B21;&#x626B;&#x63CF;&#xFF0C;&#x5F97;&#x5230;&#x6240;&#x6709;&#x9891;&#x7E41;&#x4E00;&#x9879;&#x96C6;&#x7684;&#x7684;&#x8BA1;&#x6570;&#x3002;&#x7136;&#x540E;&#x5220;&#x9664;&#x652F;&#x6301;&#x5EA6;&#x4F4E;&#x4E8E;&#x9608;&#x503C;&#x7684;&#x9879;&#xFF0C;&#x5C06;&#x9891;&#x7E41;&#x4E00;&#x9879;&#x96C6;&#x653E;&#x5165;<strong>&#x9879;&#x5934;&#x8868;</strong>&#xFF0C;&#x5E76;&#x6309;&#x7167;&#x652F;&#x6301;&#x5EA6;&#x964D;&#x5E8F;&#x6392;&#x5217;&#x3002;</li>
<li><em><strong>Step2</strong></em>&#xFF1A;&#x7B2C;&#x4E8C;&#x6B21;&#x626B;&#x63CF;&#xFF0C;&#x5C06;&#x8BFB;&#x5230;&#x7684;&#x539F;&#x59CB;&#x6570;&#x636E;&#x5254;&#x9664;&#x975E;&#x9891;&#x7E41;&#x4E00;&#x9879;&#x96C6;&#xFF0C;&#x5E76;&#x6309;&#x7167;&#x652F;&#x6301;&#x5EA6;&#x964D;&#x5E8F;&#x6392;&#x5217;&#x3002;</li>
<li><em><strong>Step3</strong></em>&#xFF1A;&#x8BFB;&#x5165;&#x6392;&#x5E8F;&#x540E;&#x7684;&#x6570;&#x636E;&#x96C6;&#xFF0C;&#x6309;&#x5E8F;&#x63D2;&#x5165;FP&#x6811;&#x3002;</li>
<li><em><strong>Step4</strong></em>&#xFF1A;&#x4ECE;<strong>&#x9879;&#x5934;&#x8868;</strong>&#x7684;&#x5E95;&#x90E8;&#x9879;&#x4F9D;&#x6B21;&#x5411;&#x4E0A;&#x6316;&#x6398;&#x3002;</li>
</ul>
<h4 class="mume-header" id="example-1">Example</h4>

<p>&#x6700;&#x5C0F;&#x652F;&#x6301;&#x5EA6;0.5</p>
<p><img src="images/relation_fptree_eg1.png" alt></p>
<p><img src="images/relation_fptree_eg1_tree.png" alt></p>

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